No, we don't generally think of the moose as a cryptid - that is, when it's on its native turf. But for some time there had been speculation that a population of introduced moose was to be found in New Zealand. Such animals had been introduced certainly, but did they still exist in the wild? There was speculation among cryptozoologists that a population might survive in the Fiordland area, but no proof. Even when K. Tustin discovered moose antlers minus their moose, it seems not to have been regarded as proof. But in 2005, he discovered some hairs which looked moose like. These were tested at Trent University in the vicinity and there now cannot be any doubt that this out of place cryptid lingers there.
The term "moose"
The moose is identical with an animal called an elk in Europe. In the United States, however, the term elk is applied to the wapiti. Isn't language confusing?